Airfoil shape for a compressor

ABSTRACT

An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in a scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

RELATED APPLICATIONS

The present application is related to the following commonly assigned applications: Ser. No. ______ (Docket No. 277752 (1011)); Ser. No. ______ (Docket No. 277754 (1013)); Ser. No. ______ (Docket No. 277765 (1014)); Ser. No. ______ (Docket No. 277784 (1012)); Ser. No. ______ (Docket No. 277913 (1016)); Ser. No. ______ (Docket No. 278957 (1015)); Ser. No. ______ (Docket No. 278976 (1017)); Ser. No. ______ (Docket No. 279149 (1019)); Ser. No. ______ (Docket No. 280088 (1020)); Ser. No. ______ (Docket No. 280098 (1021)), filed concurrently herewith. The disclosures of these applications are incorporated herein by reference in full and made a part hereof.

TECHNICAL FIELD

The present application and the resultant patent relate generally to gas turbine engines and more particularly relates to an airfoil profile or airfoil shape for use in a compressor.

BACKGROUND OF THE INVENTION

In a gas turbine engine, many system requirements should be met at each stage of the flow path therethrough to meet design goals. These design goals include, but are not limited to, overall improved efficiency, a reduction in vibratory response, improved airfoil loading capability, and the like. For example, a compressor airfoil profile should achieve thermal and mechanical operating requirements for a particular stage in the compressor. Moreover, component lifetime, reliability, and cost targets also should be met.

SUMMARY OF THE INVENTION

According to one aspect of the present application, an article of manufacture is provided with a nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

According to another aspect of the present application, an article of manufacture is provided with a suction-side nominal airfoil profile substantially in accordance with the suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y, and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil profile.

According to yet another aspect of the present application, a compressor is provided with a number of variable stator vanes, each of the variable stator vanes including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with the suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.

These and other features and improvements of the present application and the resultant patent will become apparent to one of ordinary skill in the art upon review of the following detailed description when taken in conjunction with the several drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a gas turbine engine including a compressor, a combustor, a turbine, and a load.

FIG. 2 is a schematic diagram of a compressor with multiple stages and a flow path therethrough.

FIG. 3 is a perspective view of a variable stator vane airfoil as may be described herein.

FIG. 4 is a cross-sectional view of the variable stator vane airfoil taken along line 4-4 of FIG. 3.

DETAILED DESCRIPTION

Referring now to the drawings, in which like numerals refer to like elements throughout the several views, FIG. 1 shows a schematic view of gas turbine engine 10 as may be used herein. The gas turbine engine 10 may include a compressor 15. The compressor 15 compresses an incoming flow of air 20. The compressor 15 delivers the compressed flow of air 20 to a combustor 25. The combustor 25 mixes the compressed flow of air 20 with a pressurized flow of fuel 30 and ignites the mixture to create a flow of combustion gases 35. Although only a single combustor 25 is shown, the gas turbine engine 10 may include any number of the combustors 25 arranged in a circumferential array or otherwise. The flow of combustion gases 35 is delivered in turn to a turbine 40. The flow of combustion gases 35 drives the turbine 40 so as to produce mechanical work. The mechanical work produced in the turbine 40 drives the compressor 15 via a shaft 45 and an external load 50 such as an electrical generator and the like.

The gas turbine engine 10 may use natural gas, liquid fuels, various types of syngas, and/or other types of fuels and blends thereof. The gas turbine engine 10 may be any one of a number of different gas turbine engines offered by General Electric Company of Schenectady, N.Y., including, but not limited to, those such as a 7 or a 9 series heavy duty gas turbine engine and the like. The gas turbine engine 10 may have different configurations and may use other types of components. Other types of gas turbine engines also may be used herein. Multiple gas turbine engines, other types of turbines, and other types of power generation equipment also may be used herein together.

FIG. 2 shows an example of the compressor 15. The compressor 15 may include a number of compressor stages with an axial compressor flow path 55 therethrough. As one non-limiting example only, the compressor flow path 55 may include about eighteen rotor/stator stages. The exact number of rotor and stator stages, however, may be a matter of engineering design choice and may be more or less than the illustrated eighteen stages. It is to be understood that any number of rotor and stator stages may be provided herein.

Each stage of the compressor 15 may include a number of circumferentially spaced rotor blades 60 mounted on a rotor wheel 65 and a number of circumferentially spaced stator vanes 70 attached to a static compressor case 75. Each of the rotor wheels 65 may be attached to an aft drive shaft 80, which may be connected to the turbine section of the engine. The rotor blades and stator vanes may lie in the flow path 55 of the compressor 15. The direction of airflow through the compressor flow path 55 flows generally from left to right in FIG. 2. Other components and other configurations may be used herein.

The compressor rotor blades 60 impart kinetic energy to the airflow and therefore bring about a desired pressure rise. Directly following the rotor blades 60 may be a stage of the compressor stator vanes 70. However, in some designs the stator vanes may precede the rotor blades. Both the rotor blades and stator vanes turn the airflow, slow the airflow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the airflow. Typically, multiple rows of rotor/stator stages are arranged in axial flow compressors to achieve a desired discharge to inlet pressure ratio. Each rotor blade and stator vane includes an airfoil, and these airfoils can be secured to rotor wheels or a stator case by an appropriate attachment configuration, often known as a “root,” “base” or “dovetail”. In addition, the compressor 15 also may include inlet guide vanes (IGV's) 85, variable stator vanes (VSV's) 90, and exit or exhaust guide vanes (EGV's) 95. All of these blades and vanes have airfoils that act on the medium (e.g., air) passing through the compressor flow path 55. Other components and other configurations may be used herein.

The rotor blades 60 and stator vanes 70 are merely exemplary of the stages of the compressor 15 described herein. In addition, each rotor blade 60, stator vane 70, inlet guide vane 85, variable stator vane 90, and exit guide vane 95 may be considered an article of manufacture. Further, the article of manufacture may include a variable stator vane configured for use with a compressor 15.

FIG. 3 shows an example of a variable stator vane 100 as may be described herein. In this example, the variable stator vane 100 includes an airfoil 105. Each of the variable stator vanes 100 may have an airfoil profile at any cross-section from an airfoil root 110 to an airfoil tip 120. Examples of the compressor 15 may include a variety of blades 60 and vanes 70, 85, 90, 95 arranged in multiple stages.

Referring to FIG. 4, the airfoil 105 may have a suction side 140 and a pressure side 150. The suction side 140 may be located on the opposing side of the airfoil 105 from the pressure side 150. Thus, each variable stator vane 100 may have an airfoil profile at any cross-section in the shape of the airfoil 105. The airfoil 105 also may include a leading edge 160 and a trailing edge 170 and with a chord length 180 extending therebetween. The root 110 of the airfoil 105 corresponds to the lowest non-dimensional Z value of scalable TABLE 1. The tip 120 of the airfoil 105 corresponds to the highest non-dimensional Z value of scalable TABLE 1. An airfoil 105 may extend beyond the compressor flowpath and may be tipped to achieve the desired endwall clearances. By way of example only, the airfoil may have a height from about one (1) inch to about thirty (30) inches (about 2.54 centimeters to about 76.2 centimeters) or more. Any specific airfoil height may be used herein as desired in a specific application. Other components and other configurations may be used herein.

The compressor flow path 55 requires airfoils 105 that meet system requirements of aerodynamic and mechanical blade/vane loading and efficiency. For example, it is desirable that the airfoils 105 are designed to reduce the vibratory response or vibratory stress response of the respective blades and/or vanes. Materials such as high strength alloys, non-corrosive alloys, and/or stainless steels may be used in the blades and/or vanes. To define the airfoil shape of each blade airfoil and/or vane airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and may be arrived at by iteration between aerodynamic and mechanical loadings so as to enable the turbine and compressor to run in an efficient, safe, reliable, and smooth manner. These points are unique and specific to the system. The locus that defines the airfoil profile includes a set of points with X, Y, and Z coordinates relative to a reference origin coordinate system. The three-dimensional Cartesian coordinate system of X, Y, and Z values given in scalable TABLE 1 below defines the profile of the airfoil at various locations along its length. The scalable TABLE 1 lists data for a non-coated airfoil. The envelope/tolerance for the coordinates may be about +/−5% of the chord length 180 in a direction normal to any airfoil surface location or about +/−0.25 inches (about 6.36 millimeters) in a direction normal to any airfoil surface location. However, tolerances of about +/−0.15 inches to about +/−0.25 inches (about 6.36 millimeters), or about +/−3% to about +/−5% in a direction normal to an airfoil surface location may also be used, as desired in the specific application.

A point data origin 190 may be the mid-point of the suction or pressure side of the base or tip of the airfoil, the leading edge or trailing edge of the base of the airfoil, or any other suitable location as desired. The coordinate values for the X, Y, and Z coordinates are set forth in non-dimensionalized units in scalable TABLE 1, although other units of dimensions may be used when the values are appropriately converted. As one example only, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.), a mixed number (e.g., 11/2, 101/4, etc.), and the like. The dimensional distances may be in any suitable format (e.g., inches, feet, millimeters, centimeters, meters, etc.) As one non-limiting example only, the Cartesian coordinate system has orthogonally-related X, Y, and Z axes and the X axis may lie generally parallel to the compressor rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the rotor blade tip, variable stator vane, or stator vane base. All the values in scalable TABLE 1 are given at room temperature and are unfilleted.

By defining X and Y coordinate values at selected locations in a Z direction (or height) normal to the X, Y plane, the profile section or airfoil shape of the airfoil, at each Z height along the length of the airfoil may be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each Z height may be fixed. The airfoil profiles of the various surface locations between each Z height may be determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The values in TABLE 1 may be generated and shown from zero to four or more decimal places for determining the profile of the airfoil. As the airfoil heats up the associated stress and temperature may cause a change in the X, Y, and Z values. Accordingly, the values for the profile given in TABLE 1 represent ambient, non-operating or non-hot conditions (e.g., room temperature) and may be for an uncoated airfoil.

There are typical manufacturing tolerances as well as optional coatings which may be accounted for in the actual profile of the airfoil. Each section may be joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/−values, including any coating thicknesses, are additive to the X and Y values given in TABLE 1 below. Accordingly, a distance of about +/−5% of chord length and/or +/−0.25 inches (about 6.36 millimeters) in a direction normal to a surface location along the airfoil profile defines an airfoil profile envelope for this particular airfoil design and compressor, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the TABLE 1 below at the same temperature. Additionally, a distance of about +/−5% of a chord length in a direction normal to an airfoil surface location along the airfoil profile also may define an airfoil profile envelope for this particular airfoil design. The data is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below about 3,000 RPM. The variable stator vane airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The coordinate values given in scalable TABLE 1 below provide the nominal profile for exemplary stages of a variable stator vane. Specifically, a third variable stator vane of, for example, a 9HA.01 compressor and the like:

TABLE 1 PRESSURE SIDE SUCTION SIDE X Y Z X Y Z −2.1943 3.02901 −0.5196 3.56231 −3.6077 −0.5196 −2.208 3.02381 −0.5196 3.563 −3.6061 −0.5196 −2.2245 3.01342 −0.5196 3.56421 −3.6027 −0.5196 −2.2418 2.99645 −0.5196 3.56629 −3.5959 −0.5196 −2.2582 2.9722 −0.5196 3.56889 −3.5821 −0.5196 −2.2745 2.93704 −0.5196 3.56889 −3.5601 −0.5196 −2.2887 2.88854 −0.5196 3.55659 −3.5225 −0.5196 −2.2984 2.82619 −0.5196 3.51797 −3.4868 −0.5196 −2.3021 2.75015 −0.5196 3.45717 −3.449 −0.5196 −2.2981 2.65956 −0.5196 3.38166 −3.4011 −0.5196 −2.2858 2.55391 −0.5196 3.28414 −3.3378 −0.5196 −2.2655 2.43024 −0.5196 3.17242 −3.2637 −0.5196 −2.2388 2.28804 −0.5196 3.05447 −3.183 −0.5196 −2.2054 2.12782 −0.5196 2.92318 −3.09 −0.5196 −2.1642 1.94942 −0.5196 2.7796 −2.984 −0.5196 −2.1126 1.75353 −0.5196 2.62388 −2.8646 −0.5196 −2.0494 1.54083 −0.5196 2.46402 −2.7368 −0.5196 −1.9771 1.3219 −0.5196 2.29999 −2.5998 −0.5196 −1.8952 1.09708 −0.5196 2.13233 −2.4534 −0.5196 −1.8024 0.86689 −0.5196 1.96103 −2.2977 −0.5196 −1.6981 0.63168 −0.5196 1.78644 −2.1322 −0.5196 −1.5812 0.39214 −0.5196 1.60838 −1.9567 −0.5196 −1.4508 0.14826 −0.5196 1.42721 −1.7719 −0.5196 −1.306 −0.0992 −0.5196 1.24257 −1.5779 −0.5196 −1.152 −0.3421 −0.5196 1.06019 −1.3822 −0.5196 −0.9888 −0.5808 −0.5196 0.87884 −1.1852 −0.5196 −0.8177 −0.813 −0.5196 0.69767 −0.9885 −0.5196 −0.6396 −1.0385 −0.5196 0.51615 −0.7917 −0.5196 −0.4552 −1.258 −0.5196 0.3355 −0.5943 −0.5196 −0.2643 −1.471 −0.5196 0.15779 −0.3944 −0.5196 −0.0656 −1.6768 −0.5196 −0.0163 −0.191 −0.5196 0.14185 −1.8741 −0.5196 −0.1871 0.01507 −0.5196 0.35784 −2.0629 −0.5196 −0.3552 0.22361 −0.5196 0.58214 −2.2439 −0.5196 −0.5198 0.43544 −0.5196 0.81406 −2.4173 −0.5196 −0.6798 0.65039 −0.5196 1.04339 −2.5768 −0.5196 −0.8302 0.86118 −0.5196 1.2689 −2.7228 −0.5196 −0.9705 1.06781 −0.5196 1.49008 −2.856 −0.5196 −1.1014 1.27011 −0.5196 1.70659 −2.9774 −0.5196 −1.2233 1.46757 −0.5196 1.91807 −3.0874 −0.5196 −1.3368 1.66 −0.5196 2.12453 −3.1868 −0.5196 −1.4425 1.84689 −0.5196 2.32493 −3.2763 −0.5196 −1.5408 2.02737 −0.5196 2.51944 −3.3571 −0.5196 −1.6271 2.19416 −0.5196 2.69854 −3.4257 −0.5196 −1.7031 2.34606 −0.5196 2.86135 −3.4842 −0.5196 −1.7702 2.48255 −0.5196 3.00753 −3.5332 −0.5196 −1.8287 2.60327 −0.5196 3.14592 −3.5767 −0.5196 −1.8803 2.70737 −0.5196 3.26665 −3.6124 −0.5196 −1.9269 2.79414 −0.5196 3.35983 −3.6385 −0.5196 −1.9709 2.86568 −0.5196 3.43448 −3.6586 −0.5196 −2.0126 2.92249 −0.5196 3.49129 −3.6661 −0.5196 −2.0513 2.96579 −0.5196 3.53061 −3.6493 −0.5196 −2.0864 2.99627 −0.5196 3.54776 −3.6325 −0.5196 −2.1164 3.01567 −0.5196 3.55642 −3.6198 −0.5196 −2.141 3.02624 −0.5196 3.56006 −3.6131 −0.5196 −2.163 3.03109 −0.5196 3.56162 −3.6096 −0.5196 −2.181 3.03126 −0.5196 −2.1981 2.87711 0 3.66467 −3.4343 0 −2.2111 2.87139 0 3.66537 −3.4328 0 −2.2267 2.86048 0 3.66658 −3.4295 0 −2.2427 2.84299 0 3.66831 −3.4229 0 −2.2572 2.81857 0 3.67074 −3.4092 0 −2.2711 2.78341 0 3.67004 −3.3875 0 −2.2823 2.73543 0 3.65653 −3.3513 0 −2.2886 2.67429 0 3.61739 −3.3176 0 −2.288 2.60015 0 3.55798 −3.2807 0 −2.2799 2.51234 0 3.48385 −3.2341 0 −2.2633 2.40998 0 3.38806 −3.1728 0 −2.2383 2.29046 0 3.27843 −3.1009 0 −2.2063 2.15346 0 3.16203 −3.0231 0 −2.1661 1.99913 0 3.03265 −2.9336 0 −2.1166 1.82801 0 2.89097 −2.8316 0 −2.0568 1.64008 0 2.73699 −2.7167 0 −1.9856 1.43622 0 2.5785 −2.5941 0 −1.9053 1.22664 0 2.41604 −2.4626 0 −1.815 1.01186 0 2.24941 −2.3222 0 −1.7142 0.79241 0 2.07898 −2.1729 0 −1.6021 0.56846 0 1.90474 −2.0144 0 −1.4778 0.34069 0 1.72685 −1.8469 0 −1.3406 0.10929 0 1.54499 −1.6706 0 −1.1897 −0.1252 0 1.35914 −1.4859 0 −1.0304 −0.3549 0 1.17468 −1.2999 0 −0.8626 −0.5801 0 0.99091 −1.1132 0 −0.6873 −0.7997 0 0.80731 −0.9265 0 −0.5056 −1.0126 0 0.62337 −0.7401 0 −0.318 −1.219 0 0.44011 −0.5529 0 −0.124 −1.4189 0 0.25929 −0.3634 0 0.0769 −1.6113 0 0.08158 −0.171 0 0.28562 −1.7953 0 −0.093 0.02425 0 0.50212 −1.9711 0 −0.265 0.22222 0 0.72573 −2.1393 0 −0.4337 0.42297 0 0.95575 −2.3007 0 −0.5989 0.62683 0 1.18334 −2.4502 0 −0.7545 0.82671 0 1.40712 −2.5879 0 −0.9008 1.02278 0 1.62657 −2.7145 0 −1.0378 1.21469 0 1.84134 −2.8303 0 −1.1664 1.4021 0 2.05127 −2.9357 0 −1.2866 1.58465 0 2.2553 −3.0306 0 −1.3992 1.76184 0 2.45345 −3.1161 0 −1.5045 1.93332 0 2.64519 −3.1927 0 −1.5985 2.0911 0 2.82134 −3.2582 0 −1.6822 2.23487 0 2.98103 −3.3136 0 −1.756 2.3639 0 3.12393 −3.3604 0 −1.8204 2.47839 0 3.25868 −3.4019 0 −1.8763 2.57729 0 3.37594 −3.4359 0 −1.9264 2.65956 0 3.46653 −3.4612 0 −1.9728 2.72729 0 3.5391 −3.4806 0 −2.0161 2.78115 0 3.59418 −3.4896 0 −2.0559 2.82151 0 3.63332 −3.4747 0 −2.0915 2.84992 0 3.65047 −3.4587 0 −2.1218 2.86758 0 3.65896 −3.4463 0 −2.146 2.87694 0 3.66259 −3.4397 0 −2.1677 2.88075 0 3.66398 −3.4362 0 −2.1852 2.88005 0 −2.203 2.59704 1.17502 3.89469 −3.042 1.17502 −2.2148 2.59011 1.17502 3.89521 −3.0403 1.17502 −2.2281 2.57764 1.17502 3.89625 −3.0372 1.17502 −2.2408 2.55893 1.17502 3.89798 −3.0307 1.17502 −2.2513 2.53382 1.17502 3.89989 −3.0176 1.17502 −2.2598 2.49848 1.17502 3.89833 −2.9968 1.17502 −2.2641 2.45189 1.17502 3.88326 −2.9628 1.17502 −2.2628 2.39369 1.17502 3.84394 −2.9322 1.17502 −2.2537 2.3232 1.17502 3.78644 −2.8975 1.17502 −2.2366 2.24058 1.17502 3.7149 −2.8536 1.17502 −2.2108 2.14601 1.17502 3.62206 −2.796 1.17502 −2.1761 2.03533 1.17502 3.51554 −2.7287 1.17502 −2.1328 1.90872 1.17502 3.40261 −2.6558 1.17502 −2.0792 1.76652 1.17502 3.27652 −2.5724 1.17502 −2.0147 1.60959 1.17502 3.13744 −2.4784 1.17502 −1.9394 1.43847 1.17502 2.98606 −2.3729 1.17502 −1.8512 1.25452 1.17502 2.8293 −2.2605 1.17502 −1.754 1.0659 1.17502 2.66753 −2.1408 1.17502 −1.647 0.87261 1.17502 2.50056 −2.014 1.17502 −1.5294 0.67567 1.17502 2.32892 −1.8794 1.17502 −1.4009 0.4751 1.17502 2.15242 −1.7376 1.17502 −1.2606 0.27124 1.17502 1.97107 −1.5879 1.17502 −1.1082 0.06443 1.17502 1.78505 −1.431 1.17502 −0.9429 −0.1448 1.17502 1.59418 −1.2668 1.17502 −0.7706 −0.3494 1.17502 1.40469 −1.1011 1.17502 −0.5924 −0.5478 1.17502 1.21625 −0.9343 1.17502 −0.4088 −0.7406 1.17502 1.02832 −0.7668 1.17502 −0.2201 −0.9273 1.17502 0.84056 −0.5991 1.17502 −0.0258 −1.1078 1.17502 0.65316 −0.4311 1.17502 0.17459 −1.2815 1.17502 0.46679 −0.2621 1.17502 0.38174 −1.4478 1.17502 0.28215 −0.0909 1.17502 0.59565 −1.6065 1.17502 0.09994 0.08279 1.17502 0.81614 −1.7579 1.17502 −0.0798 0.25929 1.17502 1.04183 −1.9025 1.17502 −0.257 0.43838 1.17502 1.27184 −2.0398 1.17502 −0.432 0.6199 1.17502 1.49753 −2.1664 1.17502 −0.5984 0.79761 1.17502 1.71871 −2.2834 1.17502 −0.7564 0.97168 1.17502 1.93453 −2.3913 1.17502 −0.9059 1.14194 1.17502 2.14463 −2.4905 1.17502 −1.0475 1.30804 1.17502 2.34866 −2.5816 1.17502 −1.1814 1.46999 1.17502 2.54629 −2.6651 1.17502 −1.3082 1.62674 1.17502 2.73716 −2.7413 1.17502 −1.4281 1.77847 1.17502 2.9211 −2.8109 1.17502 −1.5362 1.9179 1.17502 3.08946 −2.871 1.17502 −1.633 2.04486 1.17502 3.24188 −2.9225 1.17502 −1.7192 2.15883 1.17502 3.37819 −2.966 1.17502 −1.7956 2.25911 1.17502 3.50636 −3.0049 1.17502 −1.8621 2.34572 1.17502 3.61808 −3.0375 1.17502 −1.92 2.41777 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1.63661 −0.6894 19.5871 −0.3151 0.27211 19.5871 1.44782 −0.5513 19.5871 −0.1419 0.10756 19.5871 1.26145 −0.4096 19.5871 0.03464 −0.0532 19.5871 1.07786 −0.2648 19.5871 0.21477 −0.2101 19.5871 0.89634 −0.1176 19.5871 0.39872 −0.3629 19.5871 0.7162 0.03152 19.5871 0.58717 −0.5108 19.5871 0.5378 0.18273 19.5871 0.78046 −0.6535 19.5871 0.36131 0.33602 19.5871 0.97896 −0.7907 19.5871 0.18654 0.49156 19.5871 1.18212 −0.9225 19.5871 0.01351 0.649 19.5871 1.38928 −1.0479 19.5871 −0.1581 0.808 19.5871 1.60007 −1.1665 19.5871 −0.3281 0.96874 19.5871 1.80722 −1.275 19.5871 −0.491 1.12549 19.5871 2.01039 −1.374 19.5871 −0.6471 1.27808 19.5871 2.20923 −1.4638 19.5871 −0.7967 1.42617 19.5871 2.40305 −1.5441 19.5871 −0.9398 1.56993 19.5871 2.59167 −1.6158 19.5871 −1.0766 1.70884 19.5871 2.77475 −1.6799 19.5871 −1.2076 1.84256 19.5871 2.95159 −1.7371 19.5871 −1.3325 1.97125 19.5871 3.12185 −1.788 19.5871 −1.4464 2.08885 19.5871 3.27756 −1.8311 19.5871 −1.5502 2.19468 19.5871 3.4182 −1.8678 19.5871 −1.6434 2.28891 19.5871 3.54378 −1.8988 19.5871 −1.7258 2.37204 19.5871 3.66173 −1.9267 19.5871 −1.7973 2.44375 19.5871 3.76409 −1.9498 19.5871 −1.8585 2.50403 19.5871 3.84307 −1.9669 19.5871 −1.9117 2.55443 19.5871 3.90629 −1.9804 19.5871 −1.9581 2.59496 19.5871 3.95393 −1.9903 19.5871 −1.9979 2.62648 19.5871 3.98978 −1.9927 19.5871 −2.0312 2.64934 19.5871 4.00762 −1.983 19.5871 −2.0584 2.66493 19.5871 4.01611 −1.9728 19.5871 −2.0797 2.67411 19.5871 4.01905 −1.9669 19.5871 −2.0986 2.67896 19.5871 4.02009 −1.9638 19.5871 −2.1141 2.67879 19.5871 −2.0807 2.88248 20.269 3.93972 −2.1315 20.269 −2.089 2.8733 20.269 3.94007 −2.1299 20.269 −2.0942 2.85736 20.269 3.94059 −2.1266 20.269 −2.0951 2.83658 20.269 3.94111 −2.1204 20.269 −2.0921 2.81198 20.269 3.93938 −2.1077 20.269 −2.0849 2.77977 20.269 3.92968 −2.0902 20.269 −2.0719 2.73872 20.269 3.89833 −2.0734 20.269 −2.0525 2.68901 20.269 3.85347 −2.0572 20.269 −2.0258 2.62995 20.269 3.79354 −2.0352 20.269 −1.991 2.56101 20.269 3.71889 −2.0073 20.269 −1.9484 2.48116 20.269 3.62224 −1.97 20.269 −1.8966 2.38781 20.269 3.51104 −1.9262 20.269 −1.8355 2.28059 20.269 3.39291 −1.8782 20.269 −1.7646 2.16021 20.269 3.26093 −1.8225 20.269 −1.6832 2.02719 20.269 3.11544 −1.758 20.269 −1.59 1.88205 20.269 2.95678 −1.6837 20.269 −1.4854 1.7246 20.269 2.79276 −1.6021 20.269 −1.374 1.56179 20.269 2.62406 −1.5121 20.269 −1.2552 1.3943 20.269 2.45103 −1.4134 20.269 −1.1293 1.22231 20.269 2.27453 −1.3056 20.269 −0.9959 1.04599 20.269 2.0944 −1.1885 20.269 −0.8548 0.86585 20.269 1.91097 −1.0616 20.269 −0.7055 0.68191 20.269 1.72478 −0.9249 20.269 −0.5477 0.49485 20.269 1.53616 −0.7787 20.269 −0.3864 0.3109 20.269 1.351 −0.6284 20.269 −0.2214 0.1306 20.269 1.16931 −0.4742 20.269 −0.0521 −0.0459 20.269 0.99039 −0.3168 20.269 0.12124 −0.2186 20.269 0.81389 −0.1568 20.269 0.29913 −0.3871 20.269 0.63947 0.00572 20.269 0.48238 −0.551 20.269 0.46731 0.17095 20.269 0.67134 −0.7093 20.269 0.29757 0.33879 20.269 0.86637 −0.862 20.269 0.13008 0.50888 20.269 1.06642 −1.0081 20.269 −0.0355 0.68087 20.269 1.27115 −1.147 20.269 −0.1992 0.85442 20.269 1.48056 −1.2786 20.269 −0.3611 1.0297 20.269 1.68754 −1.3988 20.269 −0.5162 1.20048 20.269 1.8914 −1.5083 20.269 −0.6648 1.36659 20.269 2.09145 −1.6068 20.269 −0.807 1.5275 20.269 2.28735 −1.6945 20.269 −0.9429 1.68355 20.269 2.47874 −1.7724 20.269 −1.073 1.83407 20.269 2.66493 −1.8412 20.269 −1.1975 1.97887 20.269 2.84524 −1.902 20.269 −1.3164 2.11795 20.269 3.01914 −1.9555 20.269 −1.425 2.24508 20.269 3.17814 −2.0005 20.269 −1.524 2.35923 20.269 3.32225 −2.0381 20.269 −1.6132 2.4609 20.269 3.45076 −2.0695 20.269 −1.6924 2.55044 20.269 3.57166 −2.0973 20.269 −1.761 2.62787 20.269 3.6768 −2.1202 20.269 −1.8197 2.69282 20.269 3.75786 −2.137 20.269 −1.871 2.74721 20.269 3.82264 −2.15 20.269 −1.9158 2.79137 20.269 3.87148 −2.1597 20.269 −1.9544 2.82567 20.269 3.90837 −2.1625 20.269 −1.987 2.85113 20.269 3.92656 −2.1526 20.269 −2.0137 2.86862 20.269 3.93505 −2.1422 20.269 −2.0348 2.87953 20.269 3.93816 −2.1361 20.269 −2.0537 2.88577 20.269 3.9392 −2.133 20.269 −2.0696 2.88646 20.269 −1.9454 3.36226 21.6328 3.78315 −2.4696 21.6328 −1.955 3.35342 21.6328 3.78349 −2.4678 21.6328 −1.9615 3.33697 21.6328 3.78418 −2.4645 21.6328 −1.964 3.31515 21.6328 3.78453 −2.4578 21.6328 −1.9633 3.28899 21.6328 3.78211 −2.4446 21.6328 −1.9586 3.25435 21.6328 3.77119 −2.4268 21.6328 −1.9492 3.21001 21.6328 3.73759 −2.4101 21.6328 −1.9344 3.15545 21.6328 3.69013 −2.3932 21.6328 −1.9131 3.09033 21.6328 3.62674 −2.3701 21.6328 −1.8848 3.01342 21.6328 3.54793 −2.341 21.6328 −1.8498 2.92439 21.6328 3.44574 −2.3021 21.6328 −1.8074 2.81961 21.6328 3.32866 −2.2551 21.6328 −1.7572 2.69923 21.6328 3.20464 −2.2033 21.6328 −1.6986 2.56344 21.6328 3.06625 −2.1425 21.6328 −1.6307 2.41292 21.6328 2.91435 −2.071 21.6328 −1.5519 2.24803 21.6328 2.74963 −1.9874 21.6328 −1.4629 2.06876 21.6328 2.58024 −1.894 21.6328 −1.3678 1.88291 21.6328 2.4072 −1.7901 21.6328 −1.266 1.69135 21.6328 2.23175 −1.6749 21.6328 −1.1572 1.49389 21.6328 2.05421 −1.5479 21.6328 −1.0415 1.2909 21.6328 1.87529 −1.4085 21.6328 −0.9182 1.08253 21.6328 1.69585 −1.2563 21.6328 −0.7867 0.86932 21.6328 1.51728 −1.0924 21.6328 −0.6467 0.6516 21.6328 1.33888 −0.9171 21.6328 −0.5023 0.43665 21.6328 1.16567 −0.7373 21.6328 −0.3533 0.22499 21.6328 0.99645 −0.5543 21.6328 −0.1995 0.01663 21.6328 0.83017 −0.3684 21.6328 −0.0404 −0.1881 21.6328 0.66667 −0.1801 21.6328 0.12419 −0.3892 21.6328 0.50611 0.01057 21.6328 0.29428 −0.5865 21.6328 0.34866 0.20386 21.6328 0.47094 −0.7792 21.6328 0.19382 0.39976 21.6328 0.65472 −0.9663 21.6328 0.04157 0.59773 21.6328 0.84472 −1.1459 21.6328 −0.1086 0.79761 21.6328 1.04131 −1.3176 21.6328 −0.2565 0.99939 21.6328 1.24517 −1.4809 21.6328 −0.4027 1.20274 21.6328 1.44955 −1.63 21.6328 −0.5421 1.40071 21.6328 1.65411 −1.7648 21.6328 −0.675 1.59279 21.6328 1.85624 −1.8841 21.6328 −0.8018 1.77916 21.6328 2.05542 −1.9887 21.6328 −0.9227 1.95947 21.6328 2.25115 −2.0802 21.6328 −1.038 2.13354 21.6328 2.44254 −2.1595 21.6328 −1.1483 2.30068 21.6328 2.62925 −2.2286 21.6328 −1.2535 2.46142 21.6328 2.81025 −2.2886 21.6328 −1.35 2.60778 21.6328 2.97722 −2.3379 21.6328 −1.4383 2.73958 21.6328 3.1293 −2.3781 21.6328 −1.518 2.85702 21.6328 3.26526 −2.4108 21.6328 −1.5885 2.96042 21.6328 3.39326 −2.4391 21.6328 −1.6498 3.05014 21.6328 3.50463 −2.4614 21.6328 −1.7021 3.12566 21.6328 3.59054 −2.4777 21.6328 −1.748 3.18923 21.6328 3.6593 −2.4902 21.6328 −1.7883 3.24136 21.6328 3.71109 −2.4992 21.6328 −1.8235 3.28276 21.6328 3.75006 −2.5021 21.6328 −1.8535 3.31411 21.6328 3.76946 −2.4921 21.6328 −1.8782 3.33628 21.6328 3.77847 −2.4812 21.6328 −1.8985 3.35117 21.6328 3.78159 −2.4746 21.6328 −1.9169 3.36087 21.6328 3.7828 −2.4713 21.6328 −1.9331 3.36468 21.6328 −1.9021 3.50411 22.0251 3.73915 −2.5671 22.0251 −1.9122 3.49528 22.0251 3.73967 −2.5653 22.0251 −1.9191 3.47882 22.0251 3.74019 −2.562 22.0251 −1.9221 3.45665 22.0251 3.74036 −2.5551 22.0251 −1.9221 3.42998 22.0251 3.73777 −2.5418 22.0251 −1.9182 3.39465 22.0251 3.72633 −2.5238 22.0251 −1.9101 3.34927 22.0251 3.69256 −2.5068 22.0251 −1.8966 3.29349 22.0251 3.64423 −2.4898 22.0251 −1.8772 3.22646 22.0251 3.57998 −2.4668 22.0251 −1.851 3.14748 22.0251 3.49996 −2.4373 22.0251 −1.8187 3.05568 22.0251 3.39638 −2.398 22.0251 −1.779 2.9476 22.0251 3.27773 −2.3504 22.0251 −1.7321 2.82359 22.0251 3.15216 −2.2977 22.0251 −1.6773 2.68364 22.0251 3.01238 −2.2356 22.0251 −1.6132 2.5281 22.0251 2.85892 −2.1621 22.0251 −1.5391 2.35784 22.0251 2.69299 −2.076 22.0251 −1.4549 2.17251 22.0251 2.52239 −1.9797 22.0251 −1.3649 1.98043 22.0251 2.34849 −1.872 22.0251 −1.2682 1.78228 22.0251 2.1732 −1.7528 22.0251 −1.1648 1.5779 22.0251 1.99688 −1.6219 22.0251 −1.0545 1.3678 22.0251 1.82039 −1.4781 22.0251 −0.9369 1.15199 22.0251 1.64406 −1.3214 22.0251 −0.8109 0.93098 22.0251 1.46826 −1.1511 22.0251 −0.6767 0.70512 22.0251 1.29246 −0.968 22.0251 −0.538 0.4822 22.0251 1.12185 −0.7789 22.0251 −0.3947 0.26223 22.0251 0.95523 −0.5861 22.0251 −0.2463 0.04555 22.0251 0.79207 −0.3906 22.0251 −0.0927 −0.1677 22.0251 0.63185 −0.193 22.0251 0.06616 −0.3774 22.0251 0.47476 0.00727 22.0251 0.23071 −0.5835 22.0251 0.32095 0.2101 22.0251 0.40166 −0.7855 22.0251 0.17009 0.41517 22.0251 0.58024 −0.9824 22.0251 0.02165 0.62233 22.0251 0.76747 −1.1735 22.0251 −0.1244 0.83104 22.0251 0.96233 −1.3564 22.0251 −0.2683 1.04131 22.0251 1.1648 −1.5301 22.0251 −0.41 1.25297 22.0251 1.36832 −1.6882 22.0251 −0.5451 1.45873 22.0251 1.57288 −1.831 22.0251 −0.6738 1.65879 22.0251 1.77795 −1.9583 22.0251 −0.7962 1.85243 22.0251 1.98043 −2.0695 22.0251 −0.913 2.04001 22.0251 2.17927 −2.1658 22.0251 −1.0242 2.22066 22.0251 2.37395 −2.2492 22.0251 −1.1307 2.39456 22.0251 2.56378 −2.3213 22.0251 −1.2318 2.5617 22.0251 2.7479 −2.3835 22.0251 −1.3248 2.71395 22.0251 2.91781 −2.4342 22.0251 −1.4104 2.85078 22.0251 3.07231 −2.4754 22.0251 −1.4875 2.97272 22.0251 3.21105 −2.5089 22.0251 −1.5556 3.08045 22.0251 3.34182 −2.5376 22.0251 −1.6144 3.17381 22.0251 3.45561 −2.5601 22.0251 −1.6648 3.25262 22.0251 3.54343 −2.5764 22.0251 −1.709 3.31896 22.0251 3.61375 −2.5889 22.0251 −1.748 3.37369 22.0251 3.66658 −2.5979 22.0251 −1.7819 3.41716 22.0251 3.70624 −2.6003 22.0251 −1.811 3.45042 22.0251 3.72581 −2.5899 22.0251 −1.8353 3.47415 22.0251 3.73465 −2.5787 22.0251 −1.8552 3.49026 22.0251 3.73777 −2.5723 22.0251 −1.8732 3.50099 22.0251 3.7388 −2.5688 22.0251 −1.8895 3.50584 22.0251 −5.6409 4.04659 33.444 6.68173 −4.5252 33.444 −5.6506 4.02546 33.444 6.68243 −4.5222 33.444 −5.6486 3.99428 33.444 6.68329 −4.5163 33.444 −5.638 3.9567 33.444 6.68346 −4.5042 33.444 −5.6202 3.91357 33.444 6.67775 −4.4808 33.444 −5.5923 3.85797 33.444 6.65471 −4.4517 33.444 −5.5516 3.78834 33.444 6.59236 −4.4245 33.444 −5.497 3.70382 33.444 6.50766 −4.3909 33.444 −5.4272 3.60319 33.444 6.39473 −4.3462 33.444 −5.3423 3.48454 33.444 6.25357 −4.2898 33.444 −5.2412 3.34736 33.444 6.07032 −4.216 33.444 −5.1194 3.1868 33.444 5.85953 −4.1297 33.444 −4.9767 3.00338 33.444 5.63488 −4.0365 33.444 −4.8128 2.79709 33.444 5.38304 −3.9302 33.444 −4.6279 2.56794 33.444 5.10401 −3.8098 33.444 −4.4205 2.31696 33.444 4.7983 −3.6751 33.444 −4.1904 2.04503 33.444 4.48012 −3.5313 33.444 −3.9472 1.76427 33.444 4.14999 −3.3778 33.444 −3.6905 1.47553 33.444 3.80826 −3.2143 33.444 −3.4196 1.17953 33.444 3.45509 −3.0401 33.444 −3.1341 0.87659 33.444 3.09119 −2.8544 33.444 −2.8336 0.56759 33.444 2.71672 −2.6566 33.444 −2.5172 0.25305 33.444 2.33221 −2.4458 33.444 −2.1841 −0.0662 33.444 1.93851 −2.2203 33.444 −1.8448 −0.3785 33.444 1.54949 −1.987 33.444 −1.4989 −0.6836 33.444 1.16498 −1.7454 33.444 −1.1458 −0.981 33.444 0.78479 −1.4961 33.444 −0.7851 −1.2701 33.444 0.40876 −1.2396 33.444 −0.4164 −1.5504 33.444 0.03724 −0.975 33.444 −0.0391 −1.8214 33.444 −0.3284 −0.7017 33.444 0.34814 −2.0816 33.444 −0.6876 −0.4209 33.444 0.74565 −2.328 33.444 −1.041 −0.1332 33.444 1.15164 −2.5582 33.444 −1.3891 0.16056 33.444 1.56577 −2.7728 33.444 −1.7329 0.45969 33.444 1.98718 −2.9731 33.444 −2.0727 0.76314 33.444 2.40045 −3.1553 33.444 −2.398 1.06036 33.444 2.80384 −3.3221 33.444 −2.7098 1.35013 33.444 3.19581 −3.4754 33.444 −3.0084 1.63177 33.444 3.57547 −3.6165 33.444 −3.2945 1.90456 33.444 3.94267 −3.7471 33.444 −3.5684 2.16818 33.444 4.29687 −3.868 33.444 −3.8306 2.42193 33.444 4.63722 −3.9804 33.444 −4.0816 2.66545 33.444 4.96388 −4.085 33.444 −4.3109 2.8875 33.444 5.26162 −4.1777 33.444 −4.5191 3.0879 33.444 5.53009 −4.2593 33.444 −4.7058 3.26665 33.444 5.76929 −4.3301 33.444 −4.8712 3.42357 33.444 5.99394 −4.3954 33.444 −5.0155 3.55867 33.444 6.18879 −4.4512 33.444 −5.1383 3.67212 33.444 6.33879 −4.4936 33.444 −5.2443 3.76808 33.444 6.45882 −4.5272 33.444 −5.3344 3.84758 33.444 6.54906 −4.5523 33.444 −5.409 3.91236 33.444 6.61678 −4.5704 33.444 −5.4702 3.96241 33.444 6.65454 −4.5626 33.444 −5.5188 3.99896 33.444 6.67273 −4.5452 33.444 −5.5569 4.02407 33.444 6.67879 −4.5342 33.444 −5.5904 4.04191 33.444 6.68087 −4.5283 33.444 −5.6193 4.05109 33.444 −5.5937 3.85364 34.5807 6.48878 −4.7221 34.5807 −5.6027 3.83234 34.5807 6.48947 −4.7191 34.5807 −5.5997 3.80151 34.5807 6.49034 −4.7133 34.5807 −5.5885 3.76444 34.5807 6.49051 −4.7015 34.5807 −5.5703 3.72183 34.5807 6.48514 −4.6784 34.5807 −5.542 3.66692 34.5807 6.46315 −4.6492 34.5807 −5.5015 3.59799 34.5807 6.40183 −4.6218 34.5807 −5.4473 3.51398 34.5807 6.31817 −4.5885 34.5807 −5.3782 3.41387 34.5807 6.20663 −4.5442 34.5807 −5.2942 3.29609 34.5807 6.0672 −4.4884 34.5807 −5.1939 3.15961 34.5807 5.8862 −4.4157 34.5807 −5.0732 2.99991 34.5807 5.67749 −4.331 34.5807 −4.932 2.81701 34.5807 5.45544 −4.2397 34.5807 −4.7706 2.61107 34.5807 5.20603 −4.1356 34.5807 −4.5885 2.38209 34.5807 4.92994 −4.0178 34.5807 −4.385 2.13112 34.5807 4.62735 −3.8855 34.5807 −4.1593 1.85884 34.5807 4.31263 −3.744 34.5807 −3.9212 1.57721 34.5807 3.98614 −3.5924 34.5807 −3.6702 1.28674 34.5807 3.64805 −3.4303 34.5807 −3.4054 0.98831 34.5807 3.29886 −3.2569 34.5807 −3.1267 0.68208 34.5807 2.93877 −3.0716 34.5807 −2.8329 0.3691 34.5807 2.56811 −2.874 34.5807 −2.5233 0.05006 34.5807 2.18758 −2.663 34.5807 −2.1971 −0.2742 34.5807 1.79856 −2.437 34.5807 −1.864 −0.5917 34.5807 1.41526 −2.2028 34.5807 −1.5237 −0.9022 34.5807 1.03784 −1.96 34.5807 −1.1752 −1.2046 34.5807 0.6658 −1.7094 34.5807 −0.818 −1.4989 34.5807 0.29913 −1.4513 34.5807 −0.4533 −1.783 34.5807 −0.0622 −1.1849 34.5807 −0.0823 −2.0551 34.5807 −0.4171 −0.9095 34.5807 0.29601 −2.3132 34.5807 −0.7663 −0.6256 34.5807 0.68243 −2.5553 34.5807 −1.1099 −0.3345 34.5807 1.07751 −2.781 34.5807 −1.4478 −0.0374 34.5807 1.48073 −2.9911 34.5807 −1.7812 0.26483 34.5807 1.89123 −3.1871 34.5807 −2.1107 0.57123 34.5807 2.29375 −3.3657 34.5807 −2.4261 0.8707 34.5807 2.68676 −3.5296 34.5807 −2.7283 1.16221 34.5807 3.06937 −3.6808 34.5807 −3.0183 1.44522 34.5807 3.44055 −3.8209 34.5807 −3.2963 1.71889 34.5807 3.80012 −3.9505 34.5807 −3.5628 1.98268 34.5807 4.14757 −4.0707 34.5807 −3.8185 2.23642 34.5807 4.48203 −4.182 34.5807 −4.0634 2.47943 34.5807 4.80298 −4.2854 34.5807 −4.2877 2.70079 34.5807 5.09552 −4.3769 34.5807 −4.4914 2.90015 34.5807 5.35931 −4.4573 34.5807 −4.6745 3.07785 34.5807 5.59435 −4.5272 34.5807 −4.8364 3.23409 34.5807 5.81501 −4.592 34.5807 −4.9779 3.36832 34.5807 6.00623 −4.6476 34.5807 −5.0986 3.48073 34.5807 6.15363 −4.69 34.5807 −5.2031 3.57565 34.5807 6.27141 −4.7238 34.5807 −5.2918 3.65428 34.5807 6.35992 −4.7493 34.5807 −5.3655 3.71802 34.5807 6.42625 −4.7673 34.5807 −5.4258 3.76756 34.5807 6.46297 −4.7588 34.5807 −5.4736 3.80376 34.5807 6.48029 −4.7417 34.5807 −5.511 3.82887 34.5807 6.48601 −4.7309 34.5807 −5.5438 3.84706 34.5807 6.48792 −4.725 34.5807 −5.572 3.8571 34.5807 −5.541 3.76132 35.7175 6.27557 −4.9182 35.7175 −5.5498 3.74054 35.7175 6.27626 −4.9154 35.7175 −5.5465 3.71005 35.7175 6.27713 −4.9095 35.7175 −5.5353 3.67351 35.7175 6.27713 −4.8979 35.7175 −5.5173 3.63142 35.7175 6.27176 −4.875 35.7175 −5.4894 3.5772 35.7175 6.25011 −4.8458 35.7175 −5.4497 3.50896 35.7175 6.18948 −4.8184 35.7175 −5.3966 3.42565 35.7175 6.10635 −4.7858 35.7175 −5.3292 3.32606 35.7175 5.99567 −4.7422 35.7175 −5.2471 3.20897 35.7175 5.85728 −4.6874 35.7175 −5.1492 3.07318 35.7175 5.67749 −4.6159 35.7175 −5.0316 2.91418 35.7175 5.47034 −4.533 35.7175 −4.8943 2.73196 35.7175 5.2495 −4.4439 35.7175 −4.7377 2.5262 35.7175 5.00164 −4.3424 35.7175 −4.5615 2.29705 35.7175 4.72711 −4.2276 35.7175 −4.3649 2.04555 35.7175 4.42626 −4.0986 35.7175 −4.1472 1.77206 35.7175 4.11345 −3.96 35.7175 −3.9181 1.48835 35.7175 3.78938 −3.8109 35.7175 −3.677 1.19512 35.7175 3.4544 −3.6503 35.7175 −3.4231 0.8927 35.7175 3.10886 −3.4774 35.7175 −3.156 0.58197 35.7175 2.75292 −3.2921 35.7175 −2.8749 0.26327 35.7175 2.38711 −3.0934 35.7175 −2.5785 −0.0624 35.7175 2.01195 −2.8804 35.7175 −2.2659 −0.3937 35.7175 1.62934 −2.6514 35.7175 −1.9461 −0.7191 35.7175 1.25314 −2.4131 35.7175 −1.6188 −1.0375 35.7175 0.88369 −2.1658 35.7175 −1.2833 −1.3474 35.7175 0.52031 −1.9098 35.7175 −0.941 −1.6467 35.7175 0.16333 −1.6451 35.7175 −0.5915 −1.935 35.7175 −0.1872 −1.3714 35.7175 −0.2342 −2.2113 35.7175 −0.5307 −1.0881 35.7175 0.13198 −2.4739 35.7175 −0.8678 −0.7955 35.7175 0.50853 −2.7207 35.7175 −1.1986 −0.4959 35.7175 0.89564 −2.9512 35.7175 −1.5235 −0.1904 35.7175 1.2928 −3.1664 35.7175 −1.8438 0.12003 35.7175 1.69897 −3.3678 35.7175 −2.1602 0.43423 35.7175 2.0989 −3.5512 35.7175 −2.4631 0.74097 35.7175 2.49069 −3.7198 35.7175 −2.7538 1.03906 35.7175 2.87209 −3.8748 35.7175 −3.0328 1.32779 35.7175 3.24188 −4.0175 35.7175 −3.3009 1.6063 35.7175 3.59955 −4.149 35.7175 −3.5587 1.87425 35.7175 3.94509 −4.2699 35.7175 −3.8064 2.13129 35.7175 4.27782 −4.381 35.7175 −4.0442 2.37724 35.7175 4.59721 −4.4836 35.7175 −4.2622 2.60067 35.7175 4.88854 −4.5742 35.7175 −4.4609 2.80177 35.7175 5.15129 −4.6537 35.7175 −4.6393 2.98069 35.7175 5.38512 −4.7231 35.7175 −4.7974 3.13796 35.7175 5.60474 −4.7874 35.7175 −4.9358 3.27306 35.7175 5.7951 −4.8428 35.7175 −5.0543 3.38581 35.7175 5.94163 −4.8854 35.7175 −5.1568 3.4809 35.7175 6.05871 −4.9194 35.7175 −5.244 3.55971 35.7175 6.1467 −4.9448 35.7175 −5.3167 3.62328 35.7175 6.21269 −4.963 35.7175 −5.3761 3.67299 35.7175 6.24976 −4.9552 35.7175 −5.4231 3.70936 35.7175 6.26725 −4.9381 35.7175 −5.4598 3.73465 35.7175 6.27297 −4.9272 35.7175 −5.492 3.75335 35.7175 6.27487 −4.9213 35.7175 −5.5197 3.76392 35.7175 −5.4863 3.82749 36.8541 6.06339 −5.1137 36.8541 −5.4955 3.8067 36.8541 6.06391 −5.1108 36.8541 −5.4927 3.77622 36.8541 6.0646 −5.1049 36.8541 −5.4821 3.73967 36.8541 6.06426 −5.0931 36.8541 −5.465 3.69706 36.8541 6.05767 −5.0706 36.8541 −5.4385 3.6425 36.8541 6.03498 −5.042 36.8541 −5.4004 3.57322 36.8541 5.97402 −5.0152 36.8541 −5.3494 3.4887 36.8541 5.89036 −4.9831 36.8541 −5.2847 3.38737 36.8541 5.77899 −4.9402 36.8541 −5.2059 3.26821 36.8541 5.6399 −4.8863 36.8541 −5.1121 3.12982 36.8541 5.45925 −4.8158 36.8541 −4.9996 2.96735 36.8541 5.25106 −4.7337 36.8541 −4.8681 2.78098 36.8541 5.02936 −4.6455 36.8541 −4.7185 2.57019 36.8541 4.78046 −4.5447 36.8541 −4.5504 2.33532 36.8541 4.50489 −4.4306 36.8541 −4.363 2.07708 36.8541 4.20282 −4.3021 36.8541 −4.1559 1.79562 36.8541 3.88897 −4.1637 36.8541 −3.9382 1.50325 36.8541 3.56404 −4.0145 36.8541 −3.7092 1.20031 36.8541 3.22837 −3.8536 36.8541 −3.4686 0.88733 36.8541 2.88248 −3.6799 36.8541 −3.2157 0.56482 36.8541 2.52689 −3.4927 36.8541 −2.9493 0.23365 36.8541 2.16177 −3.2914 36.8541 −2.6684 −0.1053 36.8541 1.78817 −3.0742 36.8541 −2.3714 −0.4509 36.8541 1.40746 −2.8388 36.8541 −2.0667 −0.7905 36.8541 1.03525 −2.5929 36.8541 −1.7535 −1.1231 36.8541 0.67152 −2.3369 36.8541 −1.4326 −1.4459 36.8541 0.31593 −2.0719 36.8541 −1.1035 −1.7579 36.8541 −0.0314 −1.7972 36.8541 −0.7657 −2.0577 36.8541 −0.3698 −1.5123 36.8541 −0.4186 −2.3447 36.8541 −0.6992 −1.2171 36.8541 −0.061 −2.617 36.8541 −1.0207 −0.9128 36.8541 0.30848 −2.8728 36.8541 −1.3354 −0.6007 36.8541 0.6904 −3.1118 36.8541 −1.6444 −0.282 36.8541 1.08392 −3.3347 36.8541 −1.9489 0.04192 36.8541 1.48749 −3.5434 36.8541 −2.2498 0.36997 36.8541 1.88638 −3.7333 36.8541 −2.5378 0.69022 36.8541 2.2773 −3.9066 36.8541 −2.8139 1.00095 36.8541 2.65749 −4.0655 36.8541 −3.0792 1.30146 36.8541 3.02641 −4.211 36.8541 −3.3345 1.59106 36.8541 3.38391 −4.3443 36.8541 −3.5801 1.8694 36.8541 3.72928 −4.4664 36.8541 −3.8166 2.13597 36.8541 4.06218 −4.5783 36.8541 −4.0442 2.39058 36.8541 4.38209 −4.6812 36.8541 −4.2531 2.62198 36.8541 4.67394 −4.7718 36.8541 −4.4434 2.83017 36.8541 4.93721 −4.8511 36.8541 −4.6147 3.01567 36.8541 5.17156 −4.9202 36.8541 −4.7668 3.17831 36.8541 5.39153 −4.9843 36.8541 −4.9 3.31809 36.8541 5.5824 −5.0392 36.8541 −5.0139 3.435 36.8541 5.72928 −5.0811 36.8541 −5.1128 3.53356 36.8541 5.84688 −5.1147 36.8541 −5.197 3.61514 36.8541 5.93505 −5.1397 36.8541 −5.2673 3.68147 36.8541 6.00121 −5.1579 36.8541 −5.3247 3.73309 36.8541 6.0381 −5.1504 36.8541 −5.3704 3.77102 36.8541 6.05542 −5.1336 36.8541 −5.4061 3.79752 36.8541 6.06097 −5.1225 36.8541 −5.4376 3.81744 36.8541 6.0627 −5.1167 36.8541 −5.4648 3.82904 36.8541 −5.4305 3.97558 37.9906 5.85156 −5.3089 37.9906 −5.4405 3.95531 37.9906 5.85191 −5.306 37.9906 −5.4388 3.92465 37.9906 5.85243 −5.3001 37.9906 −5.4296 3.88741 37.9906 5.85139 −5.2883 37.9906 −5.414 3.84429 37.9906 5.84359 −5.266 37.9906 −5.3896 3.78834 37.9906 5.81952 −5.2381 37.9906 −5.3541 3.7175 37.9906 5.75786 −5.2121 37.9906 −5.3063 3.63055 37.9906 5.67368 −5.1807 37.9906 −5.2453 3.52646 37.9906 5.56144 −5.1386 37.9906 −5.1712 3.40365 37.9906 5.42149 −5.0858 37.9906 −5.083 3.26076 37.9906 5.23963 −5.0164 37.9906 −4.9774 3.09292 37.9906 5.03022 −4.9353 37.9906 −4.8541 2.90015 37.9906 4.80731 −4.8477 37.9906 −4.7134 2.68208 37.9906 4.5572 −4.7474 37.9906 −4.5555 2.4389 37.9906 4.28042 −4.6332 37.9906 −4.3793 2.1713 37.9906 3.97731 −4.5044 37.9906 −4.1848 1.87945 37.9906 3.66242 −4.3653 37.9906 −3.9804 1.57582 37.9906 3.33628 −4.2149 37.9906 −3.7657 1.26076 37.9906 2.99991 −4.0523 37.9906 −3.5403 0.93496 37.9906 2.65385 −3.8763 37.9906 −3.3032 0.5986 37.9906 2.29809 −3.6863 37.9906 −3.0534 0.25253 37.9906 1.93349 −3.4814 37.9906 −2.7896 −0.1018 37.9906 1.56092 −3.2599 37.9906 −2.5099 −0.4635 37.9906 1.18178 −3.019 37.9906 −2.222 −0.8193 37.9906 0.81181 −2.7661 37.9906 −1.9247 −1.1679 37.9906 0.45241 −2.5019 37.9906 −1.6169 −1.5084 37.9906 0.10236 −2.2274 37.9906 −1.2992 −1.8375 37.9906 −0.2371 −1.9413 37.9906 −0.9713 −2.1533 37.9906 −0.5655 −1.6429 37.9906 −0.6325 −2.4548 37.9906 −0.8833 −1.3326 37.9906 −0.2815 −2.7408 37.9906 −1.1917 −1.0122 37.9906 0.08297 −3.0096 37.9906 −1.4923 −0.6831 37.9906 0.46142 −3.2602 37.9906 −1.7868 −0.3473 37.9906 0.85321 −3.4937 37.9906 −2.076 −0.0059 37.9906 1.25695 −3.7118 37.9906 −2.361 0.33931 37.9906 1.65619 −3.9089 37.9906 −2.6332 0.6755 37.9906 2.04676 −4.0876 37.9906 −2.8943 1.00164 37.9906 2.42747 −4.2508 37.9906 −3.1449 1.31705 37.9906 2.79761 −4.3999 37.9906 −3.3862 1.62068 37.9906 3.15666 −4.5359 37.9906 −3.6186 1.91236 37.9906 3.50342 −4.6601 37.9906 −3.8426 2.19174 37.9906 3.83788 −4.7735 37.9906 −4.0584 2.45847 37.9906 4.15935 −4.8775 37.9906 −4.2565 2.70113 37.9906 4.45258 −4.9686 37.9906 −4.437 2.91972 37.9906 4.71724 −5.0481 37.9906 −4.5995 3.11457 37.9906 4.95315 −5.1172 37.9906 −4.7437 3.2857 37.9906 5.1745 −5.1807 37.9906 −4.87 3.43275 37.9906 5.36659 −5.2351 37.9906 −4.9784 3.55607 37.9906 5.51433 −5.2763 37.9906 −5.0723 3.66017 37.9906 5.6328 −5.3093 37.9906 −5.1522 3.74695 37.9906 5.72166 −5.3339 37.9906 −5.2188 3.81727 37.9906 5.78834 −5.3519 37.9906 −5.2736 3.87235 37.9906 5.82593 −5.346 37.9906 −5.3174 3.91288 37.9906 5.84394 −5.3292 37.9906 −5.3517 3.94145 37.9906 5.84931 −5.3181 37.9906 −5.3822 3.96293 37.9906 5.85104 −5.312 37.9906 −5.4088 3.9761 37.9906 −5.3801 4.11691 39.0299 5.65792 −5.4873 39.0299 −5.3908 4.09682 39.0299 5.65826 −5.4844 39.0299 −5.3901 4.06599 39.0299 5.65844 −5.4785 39.0299 −5.382 4.0284 39.0299 5.65688 −5.4667 39.0299 −5.3678 3.98424 39.0299 5.64787 −5.4445 39.0299 −5.3453 3.92725 39.0299 5.62258 −5.4177 39.0299 −5.312 3.85485 39.0299 5.56023 −5.3922 39.0299 −5.2672 3.76582 39.0299 5.47553 −5.3616 39.0299 −5.2097 3.65913 39.0299 5.3626 −5.3205 39.0299 −5.1397 3.53286 39.0299 5.22179 −5.2686 39.0299 −5.0565 3.38599 39.0299 5.03888 −5.2001 39.0299 −4.957 3.21313 39.0299 4.82844 −5.1199 39.0299 −4.8409 3.01429 39.0299 4.60448 −5.033 39.0299 −4.7084 2.78947 39.0299 4.35351 −4.9331 39.0299 −4.5596 2.53867 39.0299 4.07569 −4.8191 39.0299 −4.394 2.2624 39.0299 3.77189 −4.6897 39.0299 −4.2111 1.96068 39.0299 3.45613 −4.5498 39.0299 −4.0191 1.64666 39.0299 3.1293 −4.398 39.0299 −3.8176 1.32052 39.0299 2.79224 −4.2333 39.0299 −3.6058 0.98277 39.0299 2.44531 −4.0549 39.0299 −3.3832 0.63376 39.0299 2.08937 −3.8614 39.0299 −3.1483 0.2747 39.0299 1.7246 −3.6524 39.0299 −2.8998 −0.0937 39.0299 1.3536 −3.4265 39.0299 −2.6355 −0.4701 39.0299 0.97826 −3.182 39.0299 −2.3625 −0.8407 39.0299 0.61263 −2.9249 39.0299 −2.0795 −1.2045 39.0299 0.25704 −2.6549 39.0299 −1.7849 −1.5602 39.0299 −0.0887 −2.372 39.0299 −1.4793 −1.9042 39.0299 −0.4237 −2.0755 39.0299 −1.1624 −2.2347 39.0299 −0.7472 −1.7643 39.0299 −0.8328 −2.5503 39.0299 −1.0591 −1.4383 39.0299 −0.4893 −2.8496 39.0299 −1.359 −1.1016 39.0299 −0.1306 −3.1309 39.0299 −1.6482 −0.7566 39.0299 0.24439 −3.3931 39.0299 −1.929 −0.405 39.0299 0.63514 −3.6366 39.0299 −2.2032 −0.048 39.0299 1.0394 −3.8633 39.0299 −2.472 0.31298 39.0299 1.43864 −4.0669 39.0299 −2.7285 0.66459 39.0299 1.82991 −4.251 39.0299 −2.9739 1.0058 39.0299 2.21183 −4.4183 39.0299 −3.2097 1.33558 39.0299 2.58387 −4.5709 39.0299 −3.4366 1.65307 39.0299 2.94449 −4.7098 39.0299 −3.6555 1.95808 39.0299 3.29332 −4.8361 39.0299 −3.8668 2.24993 39.0299 3.62951 −4.9511 39.0299 −4.0705 2.52879 39.0299 3.95289 −5.0564 39.0299 −4.2581 2.78219 39.0299 4.2482 −5.1482 39.0299 −4.4292 3.01048 39.0299 4.51494 −5.2282 39.0299 −4.5834 3.21382 39.0299 4.7524 −5.2973 39.0299 −4.7204 3.39257 39.0299 4.97566 −5.3605 39.0299 −4.8407 3.5462 39.0299 5.16931 −5.4144 39.0299 −4.9441 3.67489 39.0299 5.31844 −5.4551 39.0299 −5.0339 3.78384 39.0299 5.43795 −5.4875 39.0299 −5.1102 3.8746 39.0299 5.52749 −5.5116 39.0299 −5.1742 3.94838 39.0299 5.59487 −5.5292 39.0299 −5.2268 4.00606 39.0299 5.63263 −5.5244 39.0299 −5.2689 4.04884 39.0299 5.65082 −5.5079 39.0299 −5.3023 4.07898 39.0299 5.65601 −5.4965 39.0299 −5.3321 4.10202 39.0299 5.65757 −5.4904 39.0299 −5.3583 4.11639 39.0299

It will be appreciated that the airfoil 105 disclosed in the above scalable TABLE 1 may be non-scaled, scaled up, or scaled down geometrically for use in other or similar turbine/compressor designs. Consequently, the coordinate values set forth in TABLE 1 may be non-scaled, scaled upwardly, or scaled downwardly such that the general airfoil profile shape remains unchanged. A scaled version of the coordinates in TABLE 1 would be represented by X, Y, and Z coordinate values of TABLE 1, with the X, Y, and Z non-dimensional coordinate values converted to inches or millimeters (or any suitable dimensional system), multiplied or divided by a constant number. The constant number may be a fraction, decimal fraction, integer or mixed number.

The disclosed airfoil shape thus may increase reliability and may be specific to the machine conditions and specifications. The airfoil shape provides a unique profile to achieve (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade or vane loadings. The disclosed loci of points allow the gas turbine and the compressor or any other suitable turbine/compressor to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled compressor.

The airfoil 105 described herein thus improves overall compressor efficiency. Specifically, the airfoil 105 may provide the desired turbine/compressor efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 105 also meets all aeromechanics, loading and stress requirements.

It should be apparent that the foregoing relates only to certain embodiments of the present application and the resultant patent. Numerous changes and modifications may be made herein by one of ordinary skill in the art without departing from the general spirit and scope of the invention as defined by the following claims and the equivalents thereof. 

We claim:
 1. An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.
 2. The article of manufacture according to claim 1, wherein the article of manufacture comprises an airfoil.
 3. The article of manufacture according to claim 1, wherein the article of manufacture comprises a variable stator vane configured for use with a compressor.
 4. The article of manufacture according to claim 1, wherein the airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to an airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to an airfoil surface location.
 5. The article of manufacture according to claim 1, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 6. The article of manufacture according to claim 1, wherein a height of the article of manufacture is about 1 inch to about 30 inches (about 2.54 centimeters to about 76.2 centimeters).
 7. An article of manufacture having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape, the X, Y, and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil profile.
 8. The article of manufacture according to claim 7, wherein the article of manufacture comprises an airfoil.
 9. The article of manufacture according to claim 7, wherein the article of manufacture comprises a variable stator vane configured for use with a compressor.
 10. The article of manufacture according to claim 7, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a suction-side airfoil surface location.
 11. The article of manufacture according to claim 7, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 12. The article of manufacture according to claim 7, wherein a height of the article of manufacture is about 1 inch to about 30 inches (about 2.54 centimeters to about 76.2 centimeters).
 13. The article of manufacture according to claim 7, further comprising the article of manufacture having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y, and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape, the X, Y, and Z values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil.
 14. A compressor comprising a plurality of variable stator vanes, each of the variable stator vanes including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.
 15. The compressor according to claim 14, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a suction-side airfoil surface location.
 16. The compressor according to claim 14, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 17. The compressor according to claim 14, wherein a height of each variable stator vane is about 1 inch to about 30 inches (about 2.54 centimeters to about 76.2 centimeters).
 18. The compressor according to claim 14, further comprising each of the plurality of variable stator vanes having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y, and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by the number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape.
 19. The compressor according to claim 18, wherein the pressure-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a pressure-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a pressure-side airfoil surface location.
 20. The compressor according to claim 18, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number. 